Investments, tenth edition

 Figure 12.1 

Prospect theory.  Panel A:  A conventional utility 

function is defined in terms of wealth and is concave, resulting 

in risk aversion.  Panel B:  Under loss aversion, the utility  function 

is defined in terms of losses relative to current wealth. It is 

also convex to the left of the origin, giving rise to risk-seeking 

 behavior in terms of losses.   

A: Conventional Utility Function

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

30

Wealth

Utility

B: Utility Function under Prospect Theory

−3

−2

−1

1

2

3

−20

−15

−10

−5

5

10

15

20

Change in Wealth

Utility

0

0

4

25

−4

−25

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7/17/13   3:46 PM

7/17/13   3:46 PM

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P A R T   I I I

  Equilibrium in Capital Markets

less risk averse as wealth increases, the function in panel B always re-centers on current 

wealth, thereby ruling out such decreases in risk aversion and possibly helping to explain 

high average historical equity risk premiums. Moreover, the convex curvature to the left of 

the origin in panel B will induce investors to be risk seeking rather than risk averse when it 

comes to losses. Consistent with loss aversion, traders in the T-bond futures contract have 

been observed to assume significantly greater risk in afternoon sessions following morning 

sessions in which they have lost money.  

13

     

 These are only a sample of many behavioral biases uncovered in the literature. Many 

have implications for investor behavior. The nearby box offers some good examples.